Erdos空间端点集的判别
Distinguishing endpoint sets from Erdős space
摘要：
证明了$f(z)=\exp(z)-1$的朱利亚集在$f$的迭代下逃逸到无穷远的所有端点的集合不同胚于有理希尔伯特空间$\mathfrak E$ .作为推论，我们证明了轨道逃逸到$\infty$或吸引到$0$的所有点$z\in \mathbb C$的集合是路径连通的。我们将这些结果推广到指数族中的许多其他函数。
英文摘要：
We prove that the set of all endpoints of the Julia set of $f(z)=\exp(z)-1$ which escape to infinity under iteration of $f$ is not homeomorphic to the rational Hilbert space $\mathfrak E$. As a corollary, we show that the set of all points $z\in \mathbb C$ whose orbits either escape to $\infty$ or attract to $0$ is path-connected. We extend these results to many other functions in the exponential family.
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